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Popular Calculus Problems

3r=(dr)/(dθ)-θ^3	3r=\frac{dr}{dθ}-θ^{3}
integral of cos(1/5 x)	\int\:\cos(\frac{1}{5}x)dx
integral of sin(x)+1	\int\:\sin(x)+1dx
derivative of ln(cosx)	\frac{d}{dx}(\ln(c)osx)
(dx)/(dt)=6xt^4	\frac{dx}{dt}=6xt^{4}
derivative of x^2-16ln(x^2)	\frac{d}{dx}(x^{2}-16\ln(x^{2}))
laplacetransform te^{-4t}	laplacetransform\:te^{-4t}
(\partial)/(\partial x)((e^{-x})/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{e^{-x}}{x^{2}+y^{2}})
y^{''}+1.5y^'+0.37y=0,y(0)=2,y^'(0)=1	y^{\prime\:\prime\:}+1.5y^{\prime\:}+0.37y=0,y(0)=2,y^{\prime\:}(0)=1
(\partial)/(\partial y)(e^{xy}cos(x^2))	\frac{\partial\:}{\partial\:y}(e^{xy}\cos(x^{2}))
sum from n=1 to infinity of 3/(n^2+5)	\sum\:_{n=1}^{\infty\:}\frac{3}{n^{2}+5}
integral of sec(6x)	\int\:\sec(6x)dx
integral of x^2e^{-10x}	\int\:x^{2}e^{-10x}dx
integral of-1/(x^3)	\int\:-\frac{1}{x^{3}}dx
limit as x approaches 5+of In(x^2-25)	\lim\:_{x\to\:5+}(In(x^{2}-25))
y^{''}+2y^'+y=t^2+1-e^t	y^{\prime\:\prime\:}+2y^{\prime\:}+y=t^{2}+1-e^{t}
derivative of 3tan(sqrt(x)+cotan(3x))	\frac{d}{dx}(3\tan(\sqrt{x})+co\tan(3x))
derivative of cos(2xy)	\frac{d}{dx}(\cos(2x)y)
area y=x^2-6,y=3	area\:y=x^{2}-6,y=3
area y=e^{3x},y=e^x,[0,2]	area\:y=e^{3x},y=e^{x},[0,2]
derivative of (24/(x^5))	\frac{d}{dx}(\frac{24}{x^{5}})
integral of x^7e^x	\int\:x^{7}e^{x}dx
y^'-3/x y=x^2	y^{\prime\:}-\frac{3}{x}y=x^{2}
f(x)=4ln(x)	f(x)=4\ln(x)
(y^')/(2yln(y))=-1/(e^x)	\frac{y^{\prime\:}}{2y\ln(y)}=-\frac{1}{e^{x}}
(\partial)/(\partial x)(9xy-4x^2y)	\frac{\partial\:}{\partial\:x}(9xy-4x^{2}y)
integral from 0 to 1 of sqrt(1+e^{2x)}	\int\:_{0}^{1}\sqrt{1+e^{2x}}dx
derivative of g(5x)=2x^2+5	derivative\:g(5x)=2x^{2}+5
integral of 1/(sqrt(x^2+8^2))	\int\:\frac{1}{\sqrt{x^{2}+8^{2}}}dx
integral from 1 to infinity of 8e^{-8x}	\int\:_{1}^{\infty\:}8e^{-8x}dx
y^'= 1/(2yt)-y/(2t)	y^{\prime\:}=\frac{1}{2yt}-\frac{y}{2t}
integral of (7x+1)(7x^2+2x)^{3/4}	\int\:(7x+1)(7x^{2}+2x)^{\frac{3}{4}}dx
integral of (-5sin(2x)-10cos(4x))	\int\:(-5\sin(2x)-10\cos(4x))dx
integral from-pi to pi of cos(3x)	\int\:_{-π}^{π}\cos(3x)dx
integral of (x-2)/(sqrt(x))	\int\:\frac{x-2}{\sqrt{x}}dx
derivative of csc(x^3+2x-tan(x))	\frac{d}{dx}(\csc(x^{3}+2x)-\tan(x))
(\partial)/(\partial z)(-y^2sin(z))	\frac{\partial\:}{\partial\:z}(-y^{2}\sin(z))
limit as x approaches-1+of (x+2x^3)^4	\lim\:_{x\to\:-1+}((x+2x^{3})^{4})
integral of (y^{3/2})^2	\int\:(y^{\frac{3}{2}})^{2}dy
y^{''}+9y=18-18e^{-t},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+9y=18-18e^{-t},y(0)=0,y^{\prime\:}(0)=0
integral of 2csc(y)(cot(y)-csc(y))	\int\:2\csc(y)(\cot(y)-\csc(y))dy
tangent of x^3+12x^2+8	tangent\:x^{3}+12x^{2}+8
derivative of 1/(ln(x+x))	\frac{d}{dx}(\frac{1}{\ln(x)+x})
derivative of (x^2/(2+x))	\frac{d}{dx}(\frac{x^{2}}{2+x})
area x^21,0,1	area\:x^{2}1,0,1
inverse oflaplace (4s^3)/((s+5)^9)	inverselaplace\:\frac{4s^{3}}{(s+5)^{9}}
limit as x approaches 2 of sqrt(5x-6)	\lim\:_{x\to\:2}(\sqrt{5x-6})
(\partial)/(\partial x)(xz+yz+xy)	\frac{\partial\:}{\partial\:x}(xz+yz+xy)
derivative of (2x^5+8/(x^3))	\frac{d}{dx}(\frac{2x^{5}+8}{x^{3}})
derivative of sqrt(15x)ln(14x)	derivative\:\sqrt{15x}\ln(14x)
sum from n=2 to infinity of (3n)/(n^2-2)	\sum\:_{n=2}^{\infty\:}\frac{3n}{n^{2}-2}
limit as x approaches 5+of (6x)/(x-5)	\lim\:_{x\to\:5+}(\frac{6x}{x-5})
integral of 3xsqrt(5x^2+1)	\int\:3x\sqrt{5x^{2}+1}dx
(dy)/(dx)=(x+sqrt(2))^2	\frac{dy}{dx}=(x+\sqrt{2})^{2}
derivative of arctan(y/x)	\frac{d}{dx}(\arctan(\frac{y}{x}))
4t(dy)/(dt)+y=t^6	4t\frac{dy}{dt}+y=t^{6}
limit as x approaches 0 of (sin(-5x))/x	\lim\:_{x\to\:0}(\frac{\sin(-5x)}{x})
integral of x^2+cos(x)	\int\:x^{2}+\cos(x)dx
derivative of 2pir	derivative\:2πr
derivative of f(x)=(2x^3+3)(x^4-2x)	derivative\:f(x)=(2x^{3}+3)(x^{4}-2x)
limit as x approaches infinity of \|x+1\|	\lim\:_{x\to\:\infty\:}(\left\|x+1\right\|)
area y=11x^2,y=x^2+7	area\:y=11x^{2},y=x^{2}+7
sum from n=1 to infinity of (1+2/n)^2e^{-5n}	\sum\:_{n=1}^{\infty\:}(1+\frac{2}{n})^{2}e^{-5n}
derivative of 5x^2-1+7e^x	derivative\:5x^{2}-1+7e^{x}
(\partial}{\partial x}(\frac{3y)/x)	\frac{\partial\:}{\partial\:x}(\frac{3y}{x})
y^{''}+6y^'+25=0	y^{\prime\:\prime\:}+6y^{\prime\:}+25=0
y^{''}+6y^'+10y=5t-2	y^{\prime\:\prime\:}+6y^{\prime\:}+10y=5t-2
integral from 1 to 3 of pi(1/x+1)^2	\int\:_{1}^{3}π(\frac{1}{x}+1)^{2}dx
y^2e^t+(e^t+2)y^'=0	y^{2}e^{t}+(e^{t}+2)y^{\prime\:}=0
integral of (x^2+4x-5)/((x^2-9)(x+1))	\int\:\frac{x^{2}+4x-5}{(x^{2}-9)(x+1)}dx
limit as x approaches infinity of 0^x	\lim\:_{x\to\:\infty\:}(0^{x})
derivative of x^4(e^x)	derivative\:x^{4}(e^{x})
(\partial)/(\partial y)(cos(z))	\frac{\partial\:}{\partial\:y}(\cos(z))
e^xy^'-e^xy=1-2x	e^{x}y^{\prime\:}-e^{x}y=1-2x
integral of (e^{4sqrt(t)})/(sqrt(t))	\int\:\frac{e^{4\sqrt{t}}}{\sqrt{t}}dt
inverse oflaplace (s-1)/(s^2(s^2+1))	inverselaplace\:\frac{s-1}{s^{2}(s^{2}+1)}
derivative of (4x^2+6x+4/(sqrt(x)))	\frac{d}{dx}(\frac{4x^{2}+6x+4}{\sqrt{x}})
limit as x approaches 7 of (\|x-7\|)/(x-7)	\lim\:_{x\to\:7}(\frac{\left\|x-7\right\|}{x-7})
xy^'+y=3x^2	xy^{\prime\:}+y=3x^{2}
integral of 2x(x^2+1)^2	\int\:2x(x^{2}+1)^{2}dx
(\partial)/(\partial x)(yln(x^4+y^3+1))	\frac{\partial\:}{\partial\:x}(y\ln(x^{4}+y^{3}+1))
area \|3x\|,x^2-10	area\:\left\|3x\right\|,x^{2}-10
derivative of (10x^3+7^{3/2})	\frac{d}{dx}((10x^{3}+7)^{\frac{3}{2}})
integral of 20x^3+1/x	\int\:20x^{3}+\frac{1}{x}dx
limit as x approaches 0 of e^{-x^2}	\lim\:_{x\to\:0}(e^{-x^{2}})
(dy)/(dx)=(x-1)/(y-3)	\frac{dy}{dx}=\frac{x-1}{y-3}
area y= 5/3 ,y= 1/(sqrt(4-x^2))	area\:y=\frac{5}{3},y=\frac{1}{\sqrt{4-x^{2}}}
d/(dt)(2+t)	\frac{d}{dt}(2+t)
integral of 2x^3+3x	\int\:2x^{3}+3xdx
derivative of ((x+5)/(x-5))^5	derivative\:(\frac{x+5}{x-5})^{5}
limit as x approaches 0+of 1/(x^2-x)	\lim\:_{x\to\:0+}(\frac{1}{x^{2}-x})
integral of x^3sqrt(7-x^2)	\int\:x^{3}\sqrt{7-x^{2}}dx
derivative of 5+sin(x)	\frac{d}{dx}(5+\sin(x))
integral of (ln(x))/(x^4)	\int\:\frac{\ln(x)}{x^{4}}dx
(\partial)/(\partial x)((x^2-y^2)/(1+x^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}-y^{2}}{1+x^{2}})
area y=2-x^2,y=6-5x	area\:y=2-x^{2},y=6-5x
f(x)=2x-3x^{2/3}	f(x)=2x-3x^{\frac{2}{3}}
tangent of y(X)=X^2+X^{-1}	tangent\:y(X)=X^{2}+X^{-1}
(\partial)/(\partial x)(xcos(x+2y))	\frac{\partial\:}{\partial\:x}(x\cos(x+2y))
(\partial)/(\partial x)(ln(y/(cos(x))))	\frac{\partial\:}{\partial\:x}(\ln(\frac{y}{\cos(x)}))

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